Conventionally, in order to place vehicles such as satellites into a particular orbit, the direction of the vehicle's thrust vector should be determined so that the vehicle moves from its present state to a desired orbital state. The process is complicated by atmospheric drag, as well as time varying mass and thrust of the launch vehicle. Typically, an open-loop trajectory optimization simulation is used to design a mission trajectory that delivers the payload to the target orbit. Without vehicle or environmental dispersions, the time dependent attitude profile could be used in the vehicle's flight computer to guide the launch vehicle to orbit. Since dispersions tend to drive the vehicle off of its preplanned trajectory, a closed-loop guidance algorithm should be used to keep the vehicle close to the preplanned trajectory.
A closed-loop guidance algorithm may enable a vehicle to reach the target orbit even when dispersions are present. A guidance algorithm calculates a vehicle attitude and attitude rate such that the vehicle will reach the correct position at the correct time with the correct velocity. Since dispersions cause variations in the time to attain the target orbit, the targeted position and velocity should be adjusted so that the desired orbit is reached at the appropriate time. The guidance problem is somewhat complicated and involves propagating both the vehicle state and target orbit state to the orbit injection point and time. The computations can involve orbit state prediction, numerical integration, iterations, matrix inversion, root finding calculations, etc. Some examples of closed-loop guidance algorithms are Delta Guidance, Q-Guidance, Cross Product Steering, Iterative Guidance Mode (“IGM”) used on Saturn launch vehicles, and Powered Explicit Guidance (“PEG”) used on the Space Shuttle. As flight computers become more capable, the guidance algorithm can become more computationally expensive.
Furthermore, conventional guidance systems generally target the orbit insertion point. However, this complicates guidance since the systems are calculating an optimized trajectory while traveling. Accordingly, a more simplified approach that reduces complexity and increases accuracy may be beneficial.